Hanganga, Pūtaiao
Ko te ture taketake o te pārōnaki, tono pāngarau
Hei timata, he mea utu te haamana'oraa e taua pārōnaki me te tikanga pāngarau e waha ana i te reira.
mahi pārōnaki Ko te hua o te mahi pärönaki o te tautohe i runga i te pārōnaki o te tautohe. Pāngarau, taea te tuhituhia tenei ariā hei faaiteraa: dy = y '* dx.
I roto i te tahuri, ki te whakatau i te pärönaki o te taurite y '= Lim dx-0 (dy / dx), a ki te whakatau i te rohe - te dy kīanga / dx = x' + α, te wahi i te α tawhā he ore rahinga pāngarau.
Na reira, kia whakanuia taha e rua o te whakapuaki i te dx, e te mutunga homai dy = y '* dx + α * dx, te wahi dx - ko te huringa ore i roto i te tautohe, (α * dx) - te uara o e taea te mahue, na dy - nuku mahi, a (y * dx) - te wahi matua o te nuku pārōnaki ranei.
mahi pārōnaki Ko te hua o te mahi pärönaki i runga i te pārōnaki o te tautohe.
Na ko reira e tika ana ki te whakaaro i te ture taketake o te pārōnaki, e maha i whakamahia i roto i te tātari pāngarau.
Ariā. nui pärönaki rite ki te moni o nga hua whiwhi i wāhanga: (he + c) = he '+ c'.
Waihoki, ka kia kaha mo te pärönaki o te rerekētanga i tēnei ture.
Ko te putanga danogo ture o pārōnaki ko te whakapae e te pärönaki o te maha o ngā rite ki te moni o nga hua whiwhi e enei ngā.
Hei tauira, ki te hiahia koe ki te kitea te pärönaki o te whakapuaki (he + c-k) ', na te hua ko te faaiteraa o te' + c 'k'.
Ariā. Ko te hua pärönaki o mahi pāngarau differentiable i te wāhi e rite ana ki te moni arā o te hua o te take tuatahi ki te rua te pārōnaki me te hua o te rua o nga take ki te pārōnaki tuatahi.
Kei te pāngarau i tuhituhia Ariā e whai ake: (he * c) '= te * he' + he '* s. Ko te putanga o te ture tauwehe ko te mutunga e kia mau ai te take tonu i roto i te pärönaki o te hua i waho te mahi pārōnaki.
I roto i te puka o te faaiteraa taurangi, tuhituhia tenei ture te whai ake nei: (he * c) = he he * ', i reira he = const.
Hei tauira, ki te hiahia koe ki te kitea te pärönaki o te faaiteraa (2a3) ', ko te hua te whakahoki: 2 * (A3) = 2 * 3 * 6 * A2 = A2.
Ariā. whanaunga pärönaki mahi rite ki te ōwehenga i waenganui i te rerekētanga o te pärönaki o te taurunga whakanuia e te tauraro me te wā taurunga te pärönaki o te tauraro me te tapawha o te tauraro.
Kei te pāngarau i tuhituhia Ariā e whai ake: (he / c) '= ( he' * he * te-c ') / 2.
I roto i te mutunga, he mea e tika ana ki te whakaaro i te tikanga mo te differentiating mahi hiato.
Ariā. Homai he fuktsii y = f (x), i reira x = c (t), na te mahi y, ki te faatura ki te t tāupe, ka karanga te matatini.
Ko te kupu, tukinotia i roto i te tātari pāngarau o te pärönaki o te mahi hiato te rite te pärönaki o te mahi whakanuia e te pärönaki o tona iti-mahi. Ko roto i te puka o te tepu hoki te haratau o te ture o te pārōnaki o ngā mahi matatini.
f (x) | f '(x) |
| (1 / s) ' | - (1/2) * c ' |
| (He c) ' | me te * (te ln te) * s ' |
| (E c) ' | e s * s ' |
| (Te ln c) ' | (1 / s) * c ' |
| (Takiuru he c) ' | 1 / (c * lg he) * c ' |
| (Te hara c) ' | cos te * s ' |
| (Koha he) ' | -sin s * s ' |
Ki te whakamahi auau o tenei tepu e ngāwari ki te mahara pärönaki. Ko te toenga o nga pärönaki o mahi matatini taea te kitea, ki te tono tatou i nga ture o te pārōnaki o ngā mahi e kua whakaturia atu i roto i nga theorems me corollaries ki a ratou.
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